The focus of this minisymposium will be high temperature reactive
systems arising in the study of high- and low-speed combustion. The
primary purpose is to bring
together a number of experts in ordinary and partial differential
equations, modellers from combustion theory, and scientific computing
specialists to discuss and share
ideas for mathematically-analytically and numerically --studying the
various combustion models. The emphasis will be on reviewing the field,
recent progress, and
areas ripe for development.

Combustion science provides a rich source for challenging
issues in
modelling and scientific computing, raising very difficult
mathematical
questions. Such questions
include: problems of well-posedness which often requires
devising new
numerical strategies, derivation and validation of asymptotic
models,
and qualitative behavior
studies such as singularity formation and instabilities.
Any listing of
topics is far from exhaustive.

Understanding such problems provides valuable information to
both the
combustion science and mathematics communities. Much progress has been
made in recent
years. For example, the treatment of the reaction-diffusion
systems
modelling low-speed flames is now almost complete.
Major progress has
been accomplished in
the understanding for new kinds of multidimensional free boundary
problems, and singular perturbation techniques have
unravelled many
intricacies of deflagration
and detonation structures including their stability properties.
Significant steps have also been taken in
understanding models involving
complex chemistry. But as more
sophisticated modeling evolves, new problems ready for development
emerge.

The idea of this conference is therefore to highlight those
combustion
models that appear both practically interesting and ripe for
mathematical development.